The sum of two angles is $89^\circ$. Angle 2 is $49^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Solution: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 89}$ ${y = 2x-49}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-49}$ for $y$ in the first equation. ${x + }{(2x-49)}{= 89}$ Simplify and solve for $x$ $ x+2x - 49 = 89 $ $ 3x-49 = 89 $ $ 3x = 138 $ $ x = \dfrac{138}{3} $ ${x = 46}$ Now that you know ${x = 46}$ , plug it back into $ {y = 2x-49}$ to find $y$ ${y = 2}{(46)}{ - 49}$ $y = 92 - 49$ ${y = 43}$ You can also plug ${x = 46}$ into $ {x+y = 89}$ and get the same answer for $y$ ${(46)}{ + y = 89}$ ${y = 43}$ The measure of angle 1 is $46^\circ$ and the measure of angle 2 is $43^\circ$.